There is increasing interest in detecting associations between rare variants and complex traits, for the following reasons: (1) the common variants identified through genome-wide association studies (GWAS) account for only a small portion of the presumed phenotypic variation and (2) the development of next-generation sequencing technology has made it feasible to directly test all rare variants. Although many statistical methods have been developed for detecting associations between rare variants and complex traits, effectively controlling for population stratification in rare variant association studies i still an open problem. Furthermore, it has been realized that every trait or disease develops over a period of time. If this developmental process is ignored, it reduces the power in rare variant association studies. However, statistical methods for longitudinal phenotypes in rare variant association studies are still underdeveloped. This project explores novel statistical methods to detect rare variants responsible for complex diseases, which include (1) a novel statistical method to control for population stratification in rare variant association studies that is applicale to a wide range of study designs, (2) novel, family-based rare variant association tests that are based on a retrospective view and thus can account for complex and undefined ascertainment of pedigrees, and (3) new rare variant association tests for longitudinal phenotypes that use growth trajectories as a phenotype instead of using phenotype values at one time point. The last specific aim of this project is to use extensive simulation studies to compare the performance of the proposed methods with that of the existing methods, apply the proposed methods to selected real data sets, and develop computer software for the proposed methods and release the software to the scientific community at no charge. If this AREA project can be funded, we will directly support two graduate research assistants majoring in statistical genetics (one full-time support and one summer support) and two part-time (summer support) senior undergraduate students. The students involved in this project will perform simulation studies and analyze real data sets. Thus, this project can increase the number of students exposed to meritorious research. The availability of funded research positions provided by this project will enable the investigators to make significant efforts toward attracting senior undergraduate and graduate students to research. Research results from this project will be also used in reports, presentations and development of short lectures for our statistical genetics seminar series and these research results presented in our seminar can stimulate the research interests of graduate students. Attracting senior undergraduate and graduate students to research and stimulating the research interests of graduate students will greatly enhance the research environment in the department.